A class of partially ordered sets called diamonds, that includes all Coxeter groups ordered by Bruhat order, is introduced. It is shown that the definition of Kazhdan-Lusztig polynomials can be generalized to the framework of diamonds, and that they can be used to construct a family of Hecke algebra representations that includes those constructed by Kazdhan and Lusztig and contains several new ones.
Diamonds and Hecke algebra representations / F. Caselli; F. Brenti; M. Marietti. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2006:(2006), pp. 1-34. [10.1155/IMRN/2006/29407]
Diamonds and Hecke algebra representations
CASELLI, FABRIZIO;
2006
Abstract
A class of partially ordered sets called diamonds, that includes all Coxeter groups ordered by Bruhat order, is introduced. It is shown that the definition of Kazhdan-Lusztig polynomials can be generalized to the framework of diamonds, and that they can be used to construct a family of Hecke algebra representations that includes those constructed by Kazdhan and Lusztig and contains several new ones.File in questo prodotto:
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